I'm using Ubuntu Mate, and I'm a slow updater; I'm still on 16.04.3 (or 16.04.5, don't recall offhand where to check system version), with HWE kernel version 4.15.0-126 generic. At present, I don't have sufficient impetus to give up a weekend of darkroom/photography time to do a complete clean reinstall, which seems to be the only reliable way to upgrade (and necessarily includes reinstalling hundreds of added packages, plus converting from repo to Snap for some, as was the case last time I upgraded GIMP). Last time I did it, it took me two days after the hardware rebuild was completed. And once done, I'd have to repeat the process for my laptop...
Something quite odd must be going on with your system. I've been using Linux (Debian) as my main OS for about 15 years (longer as an adjunct), and have never had a a problem with audio sync. If you can handle CLI apt-get and dpkg, you can probably export a list of packages you have installed, which will make it easier to re-install after a wipe or getting a new machine. I've done it a few times, but don't remember the details.
In the past I've used Mandrake (before it was Mandriva), Red Hat, CentOS, Gentoo, Ubuntu, Knoppix (installed), Puppy, DLS, and a few other distros, but I keep going back to Debian. I've even done FreeBSD, Freesbie (installed), Toms RTBT a bit (no audio or graphics), and MinuetOS. I kept having problems with Ubuntu's tendency to release the newest-latest-greatest-coolist packages without proper debugging or security vetting - it bit me a couple times. Of course, now Ubuntu seems to have wrapped social media and related crap tightly into the system.
Still, I never had audio-sync problems. NVidia always worked better for me than ATI, but neither gave me sync issues. The proprietary nVidia drivers were better than the FOSS ones - check there.
I used to prefer Gnome until Gnome3 pushed me away, then I tried Mate, but now I'm on XFCE4 (and I've dabbled with a bunch of others). You may want to check configuration in Mate or Pulse Audio (if you have it) to see if the problem is there. Also check your audio modules and configuration.
You could try a live CD just to rule out hardware issues - and to identify the modules/drivers you need and their configuration, then compare to what is on your installed system.